Forecasting

ABSTRACT

A method of generating short-, medium-range and seasonal-timescale weather or climate forecasts by running an ensemble of computer models on a distributed computing system or network. Individual model integrations are interrogated to select those that most closely ressemble observed conditions in the present and recent past and the forecast based on a weighted average of future predictions based on this subset of the ensemble. The selection criteria determining which models are deemed to fit the observations most closely may be adjusted to optimise the use of observations in forecasting specific climate variables or geographic regions in order to develop forcasts tailored to particular applications.

[0001] The present invention relates to forecasting, particularly toshort to medium term weather forecasting using an ensemble, model-basedapproach.

[0002] Techniques for weather forecasting, which are now largelycomputer-based, vary depending on the timescale required for theforecast. Short term forecasts of a few days or so use computer modelsand can be quite accurate. As for longer timescales, such as climateforecasts on longer timescales, although individual weather events areunpredictable at lead times greater than a week or so, it istheoretically possible to make more general predictions, relating to thestatistics or probability of weather events, beyond this time horizon.This is possible because there are aspects of the climate system whichvary on timescales which are longer than those of individual weatherevents that can bias their probability of occurrence. The principalclimate phenomenon which varies on timescales from seasons to years isknown as the El Nino Southern Oscillation (ENSO). ENSO involves aquasi-periodic warming and cooling of the eastern tropical Pacific seasurface, and it influences both the local and remote atmosphericcirculation patterns. ENSO has a widespread impact on world ecology,society and economics, and great effort is made to predict ENSO atseasonal lead times using both statistical and dynamical methods.

[0003] Statistical seasonal forecasting methods rely on predicting someindex of climate variability (for example the ocean temperatureanomalies in the eastern tropical Pacific—the Nino-3 index) and deducingthe local and remote impacts (so-called teleconnection patterns) usingcanonical relationships established from prior observatiois. However,often these relationships are insufficiently accurate and result inerroneous predictions.

[0004] Dynamical methods for forecasting use coupled atmosphere-oceanglobal circulation computer models (AOGCM) that solve the physicalequations of the system and represent the complex interactions betweenall aspects of the climate system. An example of such a system is thatin current use at the European Centre for Medium Range WeatherForecasting. In the accompanying drawings FIG. 1 illustrates how such acomputer model is used. Firstly, observations of the current state ofthe climate system are acquired, and these are input into the model(known as assimilation) to produce a best estimate of its current state.The model is then run forward in time to produce the forecast Asillustrated in FIG. 1, rather than running the model once, from a singleinitial state, a range of different initial states is used (byperturbing the initial state given by assimilation) so that a number offorecasts are produced which are hoped to span the range of futureweather states consistent with current information. This “ensembleinitialisation” process, though, is difficult and problematic. Forinstance, simply replacing variables in the model with the currentlyobserved values results in a model state which is very different from astate the model would generate “naturally” through its own operation.Gaps and errors in the observations and models introduce discontinuitiesfrom which unrealistically large-amplitude waves propagate as soon asthe forecast is launched. A wide range of techniques have been developedto assimilate data into models to initialise forecast with a reasonablybalanced state, but they are time-consuming and problems remain. Oneproblem is that the models have a base model climate (ie the mean annualcycle generated by running the model for a long period given only theexternal boundary conditions on the climate system) which is differentfrom the observed climate. This means that as soon as the forecast islaunched, the model begins to drift back to its own base climate. Over a10-day weather forecast, these drifts may be relatively unimportant. Butfor a seasonal time scale, the drift may be comparable or larger thanthe signals being forecast. Thus while such an approach may be usefulfor short term forecasting, it is more difficult to use for seasonalforecasting.

[0005] A traditional way to forecast the weather (as used in, forexample, the 1950's) was to examine historical weather maps forsituations which are analogous to the present conditions, referred tobelow as “analogs”, and then base a forecast on some weighted average ofthe evolution of the analog states found. This can be regarded as anexample of a method known as a “perfect ensemble” which involveschoosing analogs which are naturally in a state similar to the presentstate, and then using them for predictive purposes. However, adifficulty with this approach in weather forecasting is that the“return-time” of the atmosphere has been estimated to be of the order ofmany millions of years. That is to say forecasters would have to waitfor this length of time before having a reasonable chance of observing asingle atmospheric state consistent with the analysis on a particularday. Thus, this approach has been superseded by the use of the computermodels mentioned above.

[0006] An approach to long-term climate prediction has been proposedwhich uses distributed computing, namely the distribution of climatemodels to a plurality of personal computers, in which models are allowedto run over a period from the past to the future, and those simulationswhich are consistent with recent observed climate change are used as thebasis for ensemble forecasts of the future change. However, the climateprediction problem is fundamentally different from seasonal forecasting,because in climate prediction the main source of uncertainty lies in theresponse of the climate to changing boundary conditions: that is driverssuch as changing levels of anthropogenic greenhouse gases. However, forseasonal forecasting the main source of uncertainty is chaotic errorgrowth given possibly very small errors in the initial conditions. Thusthese are initial-condition or first-kind, prediction problems, whichare quite different from the boundary-condition or second-kindprediction problems in climate prediction.

[0007] The present invention is concerned with a method of producing aweather forecast comprising the steps of running an ensemble of coupledatmosphere-ocean global circulation computer models from differentinitial values, comparing the atmosphere-ocean states predicted by eachof the models with a corresponding set of real-world observations,selecting those model states which fit to a predetermined extent the setof observations, and producing a weather forecast from theatmosphere-ocean states subsequently predicted by the selected models.

[0008] Thus the present invention lies in applying the “perfectensemble” approach to the short to medium term forecasting problem. Itis expected to be particularly useful for seasonal forecasting. Theinventors have found that although the timescales for seasonalforecasting are long, and thus one might expect the perfect ensembleapproach (which failed for short-term forecasting) to have even moredifficulties on seasonal timescales, in fact the number of importantindependent degrees of freedom in the initial state of a seasonalforecast is lower than the number of degrees of freedom in a(short-term) atmospheric weather forecast Thus the effective return-timein a seasonal forecasting problem is likely to be relatively short formany variables of interest. This means that a seasonal forecasting modelcan be run for the equivalent of only centuries of model time to explorethe fill range of large-scale ocean-atmosphere states relevant to theseasonal forecasting problem.

[0009] With the present invention, therefore, the ensemble members arenot, themselves, constrained by direct observations of the present stateand evolution of the system, but instead a comparison with observationsover an analysis period is used to select and weight members of asub-ensemble, and the sub-ensemble is then used to make the forecast.The forecast may use a weighted average of trajectories drawn from theensemble and an estimate of anticipated forecast skill may be providedby the spread of these trajectories.

[0010] The set of real-world observations may include observations onthe near recent (within one week) state of the atmosphere-ocean system,or the past state of the atmosphere-ocean system over the length of timerelevant to the forecast phenomena of interest (this will typically becomparable or longer than the forecast lead time, so data over the pastyear would be used for six a month forecast).

[0011] The set of real-world observations may include observations ofthe current and past state of the atmosphere-ocean system, such asatmosphere winds, temperatures, pressure, cloud properties,precipitation, surface fluxes, sea level, sea surface temperatures,ocean thermal structure, salinity, soil moisture, vegetation, sea iceand derivatives thereof.

[0012] The computer model used may be selected from any suitable modelsuch as the UK Meteorological Office Unified model or the NCAR CommunityClimate System model. The initial states may be at different points onthe climate attractor of the model.

[0013] The forecast may be tailored to the requirements of a particularuser by interrogating the statistics of the ensemble model simulationsto identify skilful predictors under both general and particularregimes. For instance, it may be desired to make a seasonal forecast inrelation to only certain aspects of the climate, in which casestatistical analysis of the models' output is used to identify whichmodel variables are good predictors for the aspect of the climate ofinterest, then those models in the ensemble which have the closest matchto those predictors are used for the forecast Similarly, one may beinterested in a forecast for a particular geographical region, in whichcase skilful predictors of the weather in that region may be identified,and the models which have the closest match to the current and pastvalues of those predictors are used in the forecast. The forecast may begenerated by weighting the contribution made by each of the models inaccordance with the closeness of the fit. The fit may be judged bycriteria defined by the user. Each user may have a particular thresholdfor certain weather anomalies, and will select criteria accordingly.

[0014] Preferably the models are distributed over a plurality ofpersonal computers. This provides a great deal of computing power.Developments in personal computer technology mean that climateprediction models which formerly would only run on supercomputers, cannow be run on a conventional personal computer. Because the vastmajority of computer processors, particularly in desk-top personalcomputers, sit idle for over 90% of the time, a large number of modelscan be distributed to such personal computers (for instance owned by thegeneral public, or by medium or large organisations) to be run in theotherwise idle time of the computers. Conveniently a client-serverarrangement is used in which the server distributes the models to theclients and the clients report back to the server the results of runningthe model. The models may be left running on the clients, and when it isdesired to make a forecast, the server mines the results stored on thepersonal computers. For instance, the server may cause an additional jobto run on each client to identify whether its results to date satisfythe conditions desired for that forecasting problem and thus whether itwill be a member of the sub-ensemble. All members of the sub-ensemblethen return their subsequent results to the server for the forecast tobe generated.

[0015] The invention extends to a distributed computing systemcomprising a server and a plurality of clients as mentioned above, andalso to software for distribution to the clients for use in such adistributed computing system.

[0016] The invention will be further described by way of example withreference to the accompanying drawings in which:

[0017]FIG. 1 illustrates schematically the prior state-of-the-artensemble method of seasonal forecasting;

[0018]FIG. 2 illustrates schematically an ensemble method of seasonalforecasting in accordance with an embodiment of the present invention;

[0019]FIG. 3 illustrates a modification of the method of FIG. 2;

[0020]FIG. 4 illustrates schematically the client-server arrangement foruse in the embodiment of FIG. 3; and

[0021]FIG. 5 illustrates the results obtained by a limited version ofthe embodiment of FIG. 2.

[0022]FIG. 2 illustrates the first embodiment of the present invention.As indicated at step 20 an a-ogcm is set running from a large number ofdifferent initial conditions on around 10,000 personal computers. Thedifferent initial conditions are obtained by picking different points onthe “climate attractor” estimated from a long base-line integration ofthe model. These points are generated by performing ensembles of theorder of 100 ensemble members. Thus on a two year, 100 ensemble matrix,each will create another 100 perturbations, giving the 10,000 members.Hence, it is not necessary to run the model for 10,000 years to get10,000 sets of initial conditions.

[0023] The results of the model runs are then compared at step 22 withreal-world observations over the present and recent past. Theobservations may be of the current and past state of theatmosphere-ocean system, such as atmospheric winds, temperatures,pressure, cloud properties, precipitation, surface fluxes, sea level,sea surface temperatures, ocean thermal structure, salinity, soilmoisture, vegetation, sea ice and derivatives thereof. At step 24 asubset of the model trajectories are selected which are consistent, orshow the best consistency, with the observations. The results from thissubset of models are then used to make the seasonal forecast at step 26.The seasonal forecast may be made by combining the results of the subsetof models, and the combination may be weighted in accordance with thecloseness of the fit of the model to the observations.

[0024] It is also possible to provide an estimate of the likely accuracyof the forecast by examining whether the model trajectories in thesubset remain in close proximity to each other over the forecast period.If they do then the climatic situation is regarded as potentiallypredictable. However, if the trajectories diverge rapidly, it is clearthat the situation is not very predictable, and the forecast may be lessaccurate.

[0025] An example of the results of running a limited set of ensembleexperiments is illustrated in FIG. 5 applied to seasonal forecasts ofthe El Nino Southern Oscillation (ENSO). The black curves (v) in theFIGS. 5(a), (b) and (c) show the departures from climatology of seasurface temperature anomalies averaged in the region of 150° W-90° W, 5°S-5° N—the NINO3 index which is a good indicator of ENSO. The red curves(w) show ensemble mean forecasts of NINO3 at 3, 6 and 9 month lead timesin the 1^(st), 2^(nd) and 3^(rd) panels. The error bars show theuncertanty in the forecasts and are derived from the ensemble spread.These ensemble forecasts were achieved by searching through 380 years ofAOGCM simulations and selecting analog states based on the oceantemperatures in the upper 500 m of the tropical Pacific Ocean.Verification scores, in terms of the correlation of the forecast andobserved NINO3 index, and the root mean squared error are shown in theFIGS. 5(d) and (e) respectively. This initial application of the methodshows potential forecast skill out to 12 months.

[0026] In this case the number of simulations used to explore the“climate attractor”of the AOGCM was small and thus only limitedforecasts of the observations were possible. Increasing the number ofinitial simulations by using as many personal computers as possibleallows more regions of the attractor to be explored leading to a greater“hit rate” of analog states and a more complete set of forecasts. Also,no attempt was made systematically to optimise the algorithm used tosearch for the analog states so that skill could be improved. In orderto tailor the forecast to the individual user's needs, a further set ofAOGCM simulations can be performed based on the evolution ofmeterorological variable to which the user is most sensitive.

[0027] A modification of the above embodiment is illustrated in FIG. 3.In this embodiment aspects of the climate system which provide skilfulpredictors for a small number of key climate variables are identified.This first involves in step 30 taking the results of a number of models,for instance as generated in the above embodiment, and measuring therate of divergence of nearby model trajectories against the averageclimatological spread to see what is potentially predictable (thepredictands). Then, using an appropriate statistical technique such aslinear regression, suitable predictors can be identified for thosepredictands in step 32. These predictors then define the optimum climatevariables (for the predictand in question) that are placed in thedatabase from which the suitable analog (to the observed current weathersituation) can be drawn. It will be appreciated that for differentforecast variables different predictors may be used, but these may bedrawn from models with the same initial conditions. For example, theENSO phenomenon is known as a predictable component of the climatesystem, with its predictors being, in the first instance, the oceantemperature and heat content anomalies in the six months running up tothe forecast start. Thus in this simple case the ocean temperature andheat content anomalies are regarded as the predictors, and to make aforecast of the ENSO phenomenon, those models whose ocean temperatureand heat content anomalies match the current and recent past observedvalues of these are used in the forecast. Again, the forecast may begenerated by weighting the models in accordance with the match of thespecific predictors as illustrated at step 34. As illustrated at step36, this results in the selection of a subset of the model states. Theseasonal forecast can then be generated at step 38 using this subset ofthe model states.

[0028] A key advantage of this approach over conventional forecastingmethods is that the relative weights applied to the predictors (andhence to observations of different variables or regions) can be tailoredto the user's individual requirements at minimal additional cost. Thiswill be particularly advantageous for users who are sensitive to weathervariables or regions that are not typically given high weight in theoptimisation of conventional forecasting systems. For example, theforecast may be refined by searching for further predictors, such asatmospheric winds, temperatures, pressure, cloud properties,precipitation, surface fluxes, sea level, sea surface temperatures,ocean thermal structure, salinity, soil moisture, vegetation, sea iceand derivatives thereof.

[0029] The reliability of the ensemble forecast may be established byjudging whether the forecast indices of a particular climate variable isfound to be insensitive to the size of the base ensemble. If it is thenthe results have converged and are likely to be reliable. However if thedistribution changes as the ensemble size increases, then the resultshave not converged for that particular variable. It is also possible tomake a probabilistic forecast by selecting a number of result sequences,weighted by their proximity to the observations. Further, it is possibleto attempt to forecast historical climate events to judge thereliability of the forecast, or of course to apply known corrections forthe particular computer model used.

[0030] As mentioned above the forecast may be tailored for a particularuser. Different observations are likely to be relevant to differentspecific forecast variables. For instance, a forecast of ENSO might notbe of use for any business sensitive to European weather, as ENSO hasonly a limited impact in that region. An advantage of the presentinvention is that instead of relying on a single measure of model-datagoodness-of-fit, as forecasting centres do at present, the same ensembleof models can be interrogated repeatedly to provide optimised forecastsfor specific forecast variables such as Indian monsoon rainfall, whichmight require special attention to be paid to the model-data fit in theIndian Ocean, or north western European summer temperature, which may besensitive to north Atlantic sea surface temperatures. Thus a differentsubset of ensemble members, or a different weighting of the ensemblemembers and a different forecasting analog will be appropriate todifferent forecast indicies.

[0031] The process may be further optimised by expanding the ensemble,indicating new runs based on those members that resemble recentobservations most closely. This allows computing power to be used mosteffectively.

1. A method of producing a weather or climate forecast comprising thesteps of running an ensemble of coupled atmosphere-ocean globalcirculation computer models from different initial values, comparing theocean-atmosphere states predicted by each of the models with acorresponding set of real-world observations, selecting those modelswhich fit to a predetermined extent the set of observations, andproducing a weather forecast from the ocean-atmosphere statessubsequently predicted by the selected models.
 2. A method according toclaim 1 wherein the set of real-world observations include observationson the near recent state of the atmosphere-ocean system.
 3. A methodaccording to claim 1 or 2 wherein the set of real-world observationsinclude observations on the past state of the atmosphere-ocean system.4. A method according to claim 3 wherein the set of real-worldobservations include observations on the state of the atmosphere-oceansystem for up to 200 years.
 5. A method according to claim 3 wherein theset of real-world observations include observations on the state of theatmosphere-ocean system for up to 100 years.
 6. A method according toclaim 3 wherein the set of real-world observations include observationson the state of the atmosphere-ocean system for up to 50 years.
 7. Amethod according to claim 3 wherein the set of real-world observationsinclude observations on the state of the atmosphere-ocean system for upto 3 years.
 8. A method according to claim 3 wherein the set ofreal-world observations include observations on the state of theatmosphere-ocean system for less than one year.
 9. A method according toany one of the preceding claims wherein the set of real-worldobservations include observations on the atmospheric winds, tempertures,pressure, cloud properties, precipitation, surface fluxes, sea level,sea surface temperatures, ocean thermal structure, salinity, soilmoisture, vegetation, sea ice and derivatives thereof.
 10. A methodaccording to any one of the preceding claims wherein the ensemble ofcoupled atmosphere-ocean global circulation computer models are run frominitial states which are on different points on the attractor of theclimate model.
 11. A method according to any one of the preceding claimswherein the step of comparing the ocean-atmosphere states predicted byeach of the models with a corresponding set of real-world observationscomprises comparing predicted values of at least one of: atmosphericwinds, temperatures, pressure, cloud properties, precipitation, surfacefluxes, sea level, sea surface temperatures, ocean thermal structure,salinity, soil moisture, vegetation, sea ice and derivatives thereof.12. A method according to any one of the preceding claims wherein thestep of comparing the ocean-atmosphere states predicted by each of themodels with a corresponding set of real-world observations comprisescomparing predicted values of model variables in a selected geographicalarea with corresponding real-world observations.
 13. A method accordingto any one of the preceding claims wherein the step of comparing theocean-atmosphere states predicted by each of the models with acorresponding set of real-world observations comprises analysing themodel predictions to identify skilful predictors for one or more desiredpredictands, and wherein the models are selected on the basis of the fitbetween the identified predictors and the corresponding values in theset of real-world observations.
 14. A method according to any one of thepreceding claims wherein the weather forecast is produced by combiningthe predictions of the models with weights determined by the degree offit to the set of real-world observations.
 15. A method according to anyone of the preceding claims wherein the degree of fit is judged bycriteria tailored to specific end-users' requirements.
 16. A methodaccording to any one of the preceding claims wherein the process isfurther optimised by expanding the ensemble through initiating new runsbased on those numbers which resemble recent observations most closely.17. A method according to any one of the preceding claims wherein themodels forming the ensemble of coupled atmosphere-ocean globalcirculation computer models are distributed amongst a plurality ofcomputers.
 18. A method according to claim 17 wherein a server isprovided, said plurality of computers constituting clients of saidserver.
 19. A method according to claim 17 or 18 wherein individualmembers of the plurality of computers communicate directly with eachother to generate a forecast using peer-to-peer analysis and synthesissoftware, eliminating the need for a single control server.
 20. A methodaccording to claim 17, 18 or 19 wherein the server distributes thecoupled atmosphere-ocean global circulation computer models to theclients, and the clients report back to the server the results ofrunning the models.
 21. A method according to claim 18, 19 or 20 whereinthe step of comparing the ocean-atmosphere states predicted by each ofthe models with a corresponding set of real-world observations isconducted on the respective clients.
 22. A distributed computing systemcomprising a server and a plurality of clients constituted by personalcomputers, the server and clients being programmed by program code meansto execute the method of any one of the preceding claims.
 23. A serverand software for distribution to clients for use in a distributedcomputing system to execute the method of any one of the precedingclaims.